We study the Fisher model of a competitive market from the algorithmic perspective. For that, the related convex optimization problem due to Gale and Eisenberg, [3], is used. The latter problem is known to yield a Fisher equilibrium under some structural assumptions on consumers’ utilities, e.g. homogeneity of degree 1, homotheticity etc. We just assume the concavity of consumers’ utility functions. For this case we suggest a novel concept of Fisher-Gale equilibrium by introducing consumers’ utility prices. We develop a subgradient-type algorithm from Convex Analysis to compute a Fisher-Gale equilibrium by auction. In worst case, the number of price updates needed to achieve the ε-tolerance is proportional to (formula presented).
CITATION STYLE
Nesterov, Y., & Shikhman, V. (2015). Brief announcement: Computation of fisher-gale equilibrium by auction. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9347, pp. 312–313). Springer Verlag. https://doi.org/10.1007/978-3-662-48433-3_29
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